Levels of Measurement Pratice Questions

18. Refer to the Wage data, which reports information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.
a. Which of the 12 variables are qualitative and which are quantitative?
b. Determine the level of measurement for each variable.

Several years ago, a series of TV advertisements reported that "2 out of 3 dentists surveyed indicated they would recommend Brand X toothpaste to their patients." The implication is that 67 percent of all dentists would recommend the product to their patients. What if they surveyed only three dentists? It would certainly not be a true representation of the real situation. The trick is that the manufacturer of the toothpaste could take many surveys of three dentists and report only the surveys of three dentists in which two dentists indicated they would recommend Brand X. This is concealing the information to mislead the public. Further, a survey of more than three dentists is needed, and it must be unbiased and representative of the population of all dentists.
The term average refers to several different measures of central location that we
discuss in Chapter 3. To most people, an average is found by adding the values involved and dividing by the number of values. So if a real estate developer tells a client
An average may not be representative of all the data.that the average home in a particular subdivision sold for $150,000, we assume that
$150,000 is a representative selling price for all the homes. But suppose there are only
five homes in the subdivision and they sold for $50,000, $50,000, $60,000, $90,000,
and $500,000. We can correctly claim that the average selling price is $150,000, but
does $150,000 really seem like a "typical" selling price? Would you like to also know
that the same number of homes sold for more than $60,000 as less than $60,000? Or
that $50,000 is the selling price that occurred most frequently? So what selling price
really is the most "typical"? This example illustrates that a reported average can be
misleading, because it can be one of several numbers that could be used to represent
the data. There is really no objective set of criteria that states what average should be
reported on each occasion. We want to educate you as a consumer of data about how
a person or group might report one value that favors their position and exclude other
values. We will discuss averages, or measures of central location, in Chapter 3.
Sometimes numbers themselves can be deceptive. The mean price of homes
sold last month in the Tampa, Florida, area was $134,891.58. This sounds like a very
precise value and may instill a high degree of confidence in its accuracy. To report that the mean selling price was $135,000 doesn't convey the same precision and accuracy. However, a statistic that is very precise and carries 5 or even 10 decimal places is not necessarily accurate.

3-41 High-Low Method
Manchester Foundry produced 45,000 tons of steel in March at a cost of £1,150,000. In April, the foundry produced 35,000 tons at a cost of £950,000. Using only these two data points, determine the cost function for Manchester